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Properties

Label 2960.2
Level 2960
Weight 2
Dimension 134288
Nonzero newspaces 78
Sturm bound 1050624
Trace bound 32

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Defining parameters

Level: \( N \) = \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 78 \)
Sturm bound: \(1050624\)
Trace bound: \(32\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2960))\).

Total New Old
Modular forms 266688 136180 130508
Cusp forms 258625 134288 124337
Eisenstein series 8063 1892 6171

Trace form

\( 134288 q - 136 q^{2} - 104 q^{3} - 128 q^{4} - 254 q^{5} - 384 q^{6} - 96 q^{7} - 112 q^{8} - 28 q^{9} + O(q^{10}) \) \( 134288 q - 136 q^{2} - 104 q^{3} - 128 q^{4} - 254 q^{5} - 384 q^{6} - 96 q^{7} - 112 q^{8} - 28 q^{9} - 200 q^{10} - 292 q^{11} - 144 q^{12} - 160 q^{13} - 144 q^{14} - 118 q^{15} - 432 q^{16} - 288 q^{17} - 120 q^{18} - 52 q^{19} - 192 q^{20} - 452 q^{21} - 128 q^{22} - 72 q^{23} - 128 q^{24} - 34 q^{25} - 384 q^{26} - 116 q^{27} - 160 q^{28} - 140 q^{29} - 272 q^{30} - 380 q^{31} - 176 q^{32} - 356 q^{33} - 240 q^{34} - 182 q^{35} - 544 q^{36} - 198 q^{37} - 432 q^{38} - 148 q^{39} - 376 q^{40} - 164 q^{41} - 288 q^{42} - 88 q^{43} - 256 q^{44} - 306 q^{45} - 480 q^{46} - 32 q^{47} - 224 q^{48} - 292 q^{49} - 312 q^{50} - 252 q^{51} - 208 q^{52} - 168 q^{53} - 224 q^{54} - 122 q^{55} - 432 q^{56} + 44 q^{57} - 176 q^{58} - 52 q^{59} - 136 q^{60} - 540 q^{61} - 64 q^{62} - 160 q^{63} - 80 q^{64} - 386 q^{65} - 256 q^{66} - 208 q^{67} - 16 q^{68} - 204 q^{69} - 40 q^{70} - 412 q^{71} + 128 q^{72} + 44 q^{73} - 48 q^{74} - 536 q^{75} - 224 q^{76} - 164 q^{77} + 128 q^{78} - 284 q^{79} - 24 q^{80} - 856 q^{81} - 280 q^{83} + 144 q^{84} - 250 q^{85} - 272 q^{86} - 340 q^{87} + 80 q^{88} + 12 q^{89} + 32 q^{90} - 348 q^{91} - 144 q^{92} - 68 q^{93} - 80 q^{94} - 266 q^{95} - 336 q^{96} - 248 q^{97} - 216 q^{98} - 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2960))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2960.2.a \(\chi_{2960}(1, \cdot)\) 2960.2.a.a 1 1
2960.2.a.b 1
2960.2.a.c 1
2960.2.a.d 1
2960.2.a.e 1
2960.2.a.f 1
2960.2.a.g 1
2960.2.a.h 1
2960.2.a.i 1
2960.2.a.j 1
2960.2.a.k 1
2960.2.a.l 1
2960.2.a.m 1
2960.2.a.n 1
2960.2.a.o 2
2960.2.a.p 2
2960.2.a.q 2
2960.2.a.r 3
2960.2.a.s 3
2960.2.a.t 3
2960.2.a.u 3
2960.2.a.v 4
2960.2.a.w 5
2960.2.a.x 5
2960.2.a.y 5
2960.2.a.z 5
2960.2.a.ba 5
2960.2.a.bb 5
2960.2.a.bc 6
2960.2.d \(\chi_{2960}(2369, \cdot)\) n/a 108 1
2960.2.e \(\chi_{2960}(369, \cdot)\) n/a 112 1
2960.2.f \(\chi_{2960}(1481, \cdot)\) None 0 1
2960.2.g \(\chi_{2960}(2441, \cdot)\) None 0 1
2960.2.j \(\chi_{2960}(1849, \cdot)\) None 0 1
2960.2.k \(\chi_{2960}(889, \cdot)\) None 0 1
2960.2.p \(\chi_{2960}(961, \cdot)\) 2960.2.p.a 2 1
2960.2.p.b 2
2960.2.p.c 2
2960.2.p.d 2
2960.2.p.e 2
2960.2.p.f 4
2960.2.p.g 6
2960.2.p.h 12
2960.2.p.i 12
2960.2.p.j 12
2960.2.p.k 20
2960.2.q \(\chi_{2960}(1601, \cdot)\) n/a 152 2
2960.2.r \(\chi_{2960}(1511, \cdot)\) None 0 2
2960.2.t \(\chi_{2960}(147, \cdot)\) n/a 904 2
2960.2.v \(\chi_{2960}(1597, \cdot)\) n/a 904 2
2960.2.y \(\chi_{2960}(1437, \cdot)\) n/a 904 2
2960.2.ba \(\chi_{2960}(2147, \cdot)\) n/a 864 2
2960.2.bc \(\chi_{2960}(2399, \cdot)\) n/a 228 2
2960.2.bd \(\chi_{2960}(179, \cdot)\) n/a 904 2
2960.2.bg \(\chi_{2960}(221, \cdot)\) n/a 608 2
2960.2.bh \(\chi_{2960}(741, \cdot)\) n/a 576 2
2960.2.bk \(\chi_{2960}(339, \cdot)\) n/a 904 2
2960.2.bm \(\chi_{2960}(1153, \cdot)\) n/a 224 2
2960.2.bo \(\chi_{2960}(1183, \cdot)\) n/a 228 2
2960.2.bq \(\chi_{2960}(223, \cdot)\) n/a 216 2
2960.2.br \(\chi_{2960}(993, \cdot)\) n/a 224 2
2960.2.bt \(\chi_{2960}(857, \cdot)\) None 0 2
2960.2.bv \(\chi_{2960}(1703, \cdot)\) None 0 2
2960.2.bx \(\chi_{2960}(887, \cdot)\) None 0 2
2960.2.ca \(\chi_{2960}(697, \cdot)\) None 0 2
2960.2.cc \(\chi_{2960}(931, \cdot)\) n/a 608 2
2960.2.ce \(\chi_{2960}(149, \cdot)\) n/a 864 2
2960.2.cf \(\chi_{2960}(1109, \cdot)\) n/a 904 2
2960.2.ch \(\chi_{2960}(771, \cdot)\) n/a 608 2
2960.2.ck \(\chi_{2960}(31, \cdot)\) n/a 152 2
2960.2.cl \(\chi_{2960}(667, \cdot)\) n/a 864 2
2960.2.cn \(\chi_{2960}(117, \cdot)\) n/a 904 2
2960.2.cq \(\chi_{2960}(413, \cdot)\) n/a 904 2
2960.2.cs \(\chi_{2960}(1627, \cdot)\) n/a 904 2
2960.2.ct \(\chi_{2960}(919, \cdot)\) None 0 2
2960.2.cx \(\chi_{2960}(1121, \cdot)\) n/a 152 2
2960.2.cy \(\chi_{2960}(729, \cdot)\) None 0 2
2960.2.cz \(\chi_{2960}(249, \cdot)\) None 0 2
2960.2.dc \(\chi_{2960}(841, \cdot)\) None 0 2
2960.2.dd \(\chi_{2960}(121, \cdot)\) None 0 2
2960.2.di \(\chi_{2960}(529, \cdot)\) n/a 224 2
2960.2.dj \(\chi_{2960}(1009, \cdot)\) n/a 224 2
2960.2.dk \(\chi_{2960}(81, \cdot)\) n/a 456 6
2960.2.dl \(\chi_{2960}(119, \cdot)\) None 0 4
2960.2.do \(\chi_{2960}(27, \cdot)\) n/a 1808 4
2960.2.dq \(\chi_{2960}(917, \cdot)\) n/a 1808 4
2960.2.dr \(\chi_{2960}(837, \cdot)\) n/a 1808 4
2960.2.dt \(\chi_{2960}(507, \cdot)\) n/a 1808 4
2960.2.dw \(\chi_{2960}(911, \cdot)\) n/a 304 4
2960.2.dx \(\chi_{2960}(51, \cdot)\) n/a 1216 4
2960.2.dz \(\chi_{2960}(989, \cdot)\) n/a 1808 4
2960.2.ec \(\chi_{2960}(269, \cdot)\) n/a 1808 4
2960.2.ee \(\chi_{2960}(251, \cdot)\) n/a 1216 4
2960.2.eg \(\chi_{2960}(97, \cdot)\) n/a 448 4
2960.2.eh \(\chi_{2960}(47, \cdot)\) n/a 456 4
2960.2.ej \(\chi_{2960}(767, \cdot)\) n/a 456 4
2960.2.el \(\chi_{2960}(177, \cdot)\) n/a 448 4
2960.2.en \(\chi_{2960}(393, \cdot)\) None 0 4
2960.2.eq \(\chi_{2960}(1047, \cdot)\) None 0 4
2960.2.es \(\chi_{2960}(343, \cdot)\) None 0 4
2960.2.eu \(\chi_{2960}(473, \cdot)\) None 0 4
2960.2.ew \(\chi_{2960}(939, \cdot)\) n/a 1808 4
2960.2.ex \(\chi_{2960}(581, \cdot)\) n/a 1216 4
2960.2.fa \(\chi_{2960}(101, \cdot)\) n/a 1216 4
2960.2.fb \(\chi_{2960}(859, \cdot)\) n/a 1808 4
2960.2.fe \(\chi_{2960}(319, \cdot)\) n/a 456 4
2960.2.fg \(\chi_{2960}(787, \cdot)\) n/a 1808 4
2960.2.fi \(\chi_{2960}(717, \cdot)\) n/a 1808 4
2960.2.fj \(\chi_{2960}(637, \cdot)\) n/a 1808 4
2960.2.fl \(\chi_{2960}(307, \cdot)\) n/a 1808 4
2960.2.fn \(\chi_{2960}(711, \cdot)\) None 0 4
2960.2.fr \(\chi_{2960}(289, \cdot)\) n/a 672 6
2960.2.fs \(\chi_{2960}(321, \cdot)\) n/a 456 6
2960.2.fu \(\chi_{2960}(49, \cdot)\) n/a 672 6
2960.2.fw \(\chi_{2960}(169, \cdot)\) None 0 6
2960.2.fy \(\chi_{2960}(201, \cdot)\) None 0 6
2960.2.gb \(\chi_{2960}(9, \cdot)\) None 0 6
2960.2.gd \(\chi_{2960}(41, \cdot)\) None 0 6
2960.2.ge \(\chi_{2960}(457, \cdot)\) None 0 12
2960.2.gh \(\chi_{2960}(351, \cdot)\) n/a 912 12
2960.2.gi \(\chi_{2960}(7, \cdot)\) None 0 12
2960.2.gl \(\chi_{2960}(247, \cdot)\) None 0 12
2960.2.gm \(\chi_{2960}(79, \cdot)\) n/a 1368 12
2960.2.gp \(\chi_{2960}(57, \cdot)\) None 0 12
2960.2.gq \(\chi_{2960}(13, \cdot)\) n/a 5424 12
2960.2.gs \(\chi_{2960}(21, \cdot)\) n/a 3648 12
2960.2.gv \(\chi_{2960}(229, \cdot)\) n/a 5424 12
2960.2.gx \(\chi_{2960}(133, \cdot)\) n/a 5424 12
2960.2.gy \(\chi_{2960}(83, \cdot)\) n/a 5424 12
2960.2.hb \(\chi_{2960}(3, \cdot)\) n/a 5424 12
2960.2.hd \(\chi_{2960}(531, \cdot)\) n/a 3648 12
2960.2.hf \(\chi_{2960}(19, \cdot)\) n/a 5424 12
2960.2.hg \(\chi_{2960}(59, \cdot)\) n/a 5424 12
2960.2.hi \(\chi_{2960}(91, \cdot)\) n/a 3648 12
2960.2.hl \(\chi_{2960}(123, \cdot)\) n/a 5424 12
2960.2.hm \(\chi_{2960}(67, \cdot)\) n/a 5424 12
2960.2.hp \(\chi_{2960}(573, \cdot)\) n/a 5424 12
2960.2.hr \(\chi_{2960}(189, \cdot)\) n/a 5424 12
2960.2.hs \(\chi_{2960}(181, \cdot)\) n/a 3648 12
2960.2.hu \(\chi_{2960}(533, \cdot)\) n/a 5424 12
2960.2.hx \(\chi_{2960}(17, \cdot)\) n/a 1344 12
2960.2.hy \(\chi_{2960}(39, \cdot)\) None 0 12
2960.2.ia \(\chi_{2960}(287, \cdot)\) n/a 1368 12
2960.2.id \(\chi_{2960}(127, \cdot)\) n/a 1368 12
2960.2.if \(\chi_{2960}(311, \cdot)\) None 0 12
2960.2.ig \(\chi_{2960}(753, \cdot)\) n/a 1344 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2960)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(740))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1480))\)\(^{\oplus 2}\)